Displaying similar documents to “Certain mean values and non-vanishing of automorphic L-functions with large level”

Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series

D. A. Goldston, S. M. Gonek (1998)

Acta Arithmetica

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We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications be removed from the final result. Similar results are obtained for the tails of Dirichlet series....